Computation of cones of generalized supporting functionals (Q1116081)

This note proposes another approach to the construction of cones of generalized supporting functionals. It is shown that in a number of cases cones of generalized supporting functionals coincide (up to sign) with the conjugate cones of the conical hulls of some sets, and for some classes of functionals with the conjugate cones of directions of decrease [\textit{I. V. Girsanov}, Lectures on mathematical theory of extremum problems (Russian), Moscow State Univ. (Moscow 1970), p. 38; for a review of the 1972 English translation see Zbl 0234.49016] and forbidden variations [\textit{A. Ya. Dubovitskij} and \textit{A. A. Milyutin}, Zh. Vychisl. Mat. Mat. Fiz. 5, 395-453 (1965; Zbl 0158.335)]. Since the procedure for the construction of these cones has been developed to a certain extent, generalized supporting functionals in these special cases can be described in terms of previous results.